Start to snigger and make fun of garment (5)
I believe the answer is:
smock
'garment' is the definition.
(I know that smock is a type of garment)
'start to snigger and make fun of' is the wordplay.
'start to' indicates taking the first letters.
'and' is a charade indicator (letters next to each other).
'make fun of' becomes 'mock' (to make fun of someone is to mock or tease them).
The initial letter of 'snigger' is 's'.
's'+'mock'='SMOCK'
(Other definitions for smock that I've seen before include "Artist's loose overall" , "Artist's, peasant's, overall" , "Loose dress or blouse" , "artist's attire" , "Loose overall or dress" .)